Congruences,equational theories and lattice representations

We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.To László Fuchs on the occasion of his 70th birthday     

Velocity inversion: A case study in infinite-dimensional optimization

The goal of seismic velocity inversion is the estimation of seismic wave velocities inside the earth by attempting to predict, in a least-error sense, seismic waveforms measured at its surface. We present velocity inversion as a case study in the various infinite-dimensional pathologies which may afflict practically important problems of distributed parameter identification, treated as optimization problems in function spaces. These features differentiate various problem formulations far beyond the degree one would expect for finite- (small-) dimensional problems. We illustrate this differentiation by comparing the characteristics of three different least-squares formulations of velocity inversion.     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

15N-NMR spectroscopy. III. Neighboring residue effects in sequence polymers containing glycylglycine units

The tripeptides Phe-Gly-Gly, β-Ala-Gly-Gly, and ?-Aca-Gly-Gly as well as the peptide derivatives δ-isothiocyanatovaleroyl-Gly-Gly and ?-isothiocyanatocaproyl-Gly-Gly were synthesized by using known methods so that the peptide nitrogen between the two glycyl residues was isotopically enriched in ¹⁵N to a level of 0.8–0.9%. These monomer units were then used to produce the sequence polymers (Phe-Gly-Gly)_n, (β-Ala-Gly-Gly)_n, (δ-Ava-Gly-Gly)_n, and (?-Aca-Gly-Gly)_n. The 18.24 MHz ¹⁵N-NMR spectra of the oligo- and polypeptides were obtained by using trifluoroacetic acid as solvent, since the solutions have relatively low viscosity and exhibit a strong negative nuclear Overhauser enhancement of the ¹⁵N signals. For comparison, ¹⁵N-NMR spectra of the homopolymers (Gly)_n, (β-Ala)_n, (γ-Abu)_n, (δ-Ava)_n, and (?-Aca)_n were also recorded. The ¹⁵N signals from the ω-aminoacyl residues in the sequence polymers appear up to 11 ppm upfield of the signals observed for the homopolyamides. The ¹⁵N signals from the two glycyl residues are separated by 3–7 ppm. Comparison with the ¹³C-NMR spectra of the same polymers indicates that ¹⁵N-NMR is better suited for the characterization and sequence analysis of these types of polymers.     

INTERACTION OF VIOLOGEN DYES WITH CHROMATOPHORES AND REACTION-CENTER PREPARATIONS FROM RHODOSPIRILLUM RUBRUM

Abstract —Various low-potential viologen dyes enhance light-induced absorption changes in the near-infrared region (ΔA870) in chromatophore preparations from Rhodospirillum rubrum in the presence of dichlorophenol indophenol and a high concentration of ascorbate (DCPIP + asc). An increase in ΔA870 was also observed in large reaction-center preparations from R. rubrum with viologens in the presence of ascorbate. Our results indicate that E'₀, of the primary electron acceptor X may be as low as -0.37 V, as suggested recently by P. A. Loach (1973, personal communication).     

Vertical excitation as a transient phenomenon

For a particular model with two electronic states, each with two vibrations, the dipole correlation function governing electronic absorption is e ^?iωOt cosγt with spectrum ω ₀±γ. The function starts as e ^?iωOt (γ?ω ₀), with Fourier transform peaking around ω ₀ instead of ω ₀±γ, and this is associated with vertical excitation. After a time t～2/γ the spectrum goes over into the normal one. As a generalization, a procedure is outlined for characterizing the state reached first after interaction with light is initiated. Finally it is suggested that one can understand aspects of internal conversion by analogy with the case of vertical excitation.     

Triazine chemistry VIII. 2,5-dihydro-5-oxo-1,2,4-triazines

2,5-Dihydro-5-oxo-1,2,4-triazine and some of its alkylated derivatives have been prepared. Nmr spectroscopic analysis has established that the 2,5-dihydro-5-oxo tautomers are preferred over the 4,5-dihydro-5-oxo ones. This preference, and the behavior of 1,2,4-triazines in some other chemical reactions has been interpreted in terms of electron-electron repulsions between the lone pairs of electrons of N₁ and N₂ in this ring system.     

The foam analogy: from phases to elasticity

By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic properties of such colloidal crystals and consider the face-centered cubic, body-centered cubic and A15 lattices. We discuss two types of soft interparticle potentials corresponding to charged and fuzzy colloids, respectively, and we analyze the dependence of the elastic constants on density as well as on the parameters of the potential. We show that the bulk moduli of the three lattices are generally quite similar, and that the shear moduli of the two non-close-packed lattices are considerably smaller than in the face-centered cubic lattice. We find that in charged colloids, the elastic constants are the largest at a finite screening length, and we discuss a shear instability of the A15 lattice.     

Engineering cytochrome P-450s

Cytochrome P-450 isozymes represent a critical component of nature’s spectrum of detoxification catalysts that could be exploited for bioremediation. The ethanol-inducible human cytochrome P-450 2E1 serves as a model eukaryotic P-450 that complements the bacterial P-450 cam in dehalogenation and detoxification of environmental pollutants. We explored the construction of novel chimeric P-450s using cytochrome P-450 camC and 2E1 genes. For construction of chimera 1 (478 amino acids, 55.14 kDa), 145 amino acids from the N-terminus of P-450 2E1 protein (493 amino acids, 56.84 kDa) were replaced with 130 amino acids from the N-terminus of P-450 camC protein (415 amino acids, 46.66 kDa). In chimera 2 (525 amino acids, 60.24 kDa) the strategy involves replacement of 28 amino acids in the C-terminus of chimera 1 with 75 amino acids from the C-terminus of P-450 camC gene. Homology models of both the chimeric proteins were developed using SWISS-MODEL based on the known crystal structure of cytochrome P-450 camC, BM-3, 1DT6A, and 2C17A. The models indicated that the proposed heme-binding site was intact, which is inevitable for catalytic activity of cytochrome P-450s. The expression of chimera 1 and 2 genes in Escherichia coli DH5α was evident from light-pink cell pellets, protein band in sodium dodecyl sulfate polyacrylamide gel electrophoresis, and diagnostic carbon monoxide-difference spectra. Our studies show that strategies can be developed to exploit the natural diversity of the P-450 superfamily to generate chimeric biocatalysts that would provide new templates amenable to directed evolution.